Primary victories by candidates supported by the conservative movement could point to a new path for Republicans. Or they could give Democrats a boost and push the GOP back to the middle.

Reporting from Washington — By winning the Republican nomination for Delaware's Senate seat Tuesday, the "tea party" movement concluded the primary season with eight Senate nominations, shocking the GOP establishment and pushing the party well to the right.

FOR THE RECORD: 'Tea party' wins: An article in the Sept. 16 Section A about primary election victories by the "tea party" movement included a reference to Sen. Tim Kaine, chairman of the Democratic Senatorial Campaign Committee. Kaine is not a senator, and the committee he chairs is the Democratic National Committee. Now the tea party juggernaut faces its biggest test: Will those primary winners be able to ride the anti-incumbent mood to victory in November, or will they create new chances for Democrats to hold on to congressional majorities?

All of these candidates — Christine O'Donnell of Delaware, Joe Miller of Alaska, Mike Lee of Utah, Rand Paul of Kentucky, Sharron Angle of Nevada, Marco Rubio of Florida, Ken Buck of Colorado and Ron Johnson of Wisconsin — have called for a repeal of President Obama's healthcare bill. Some have advocated deep changes to Social Security, eliminating the Department of Education, cutting environmental regulation and withdrawing from the United Nations.

Democrats believe these candidates have helped cement an image of GOP extremism out of step with voters.

The stakes are also high for the GOP itself. A cluster of general election successes for tea party candidates would invigorate those who want to push the Republican Party to the right, to reduce the size and mission of the federal government and to compromise less. Tea party losses in key races, meanwhile, could shift the momentum back to those favoring more ideological diversity in the party.

The battle between the factions has been waging for years — but rarely has it been so public than this election season.

On Tuesday night, Republican strategist Karl Rove criticized O'Donnell, his party's nominee in Delaware, for what he called "nutty" statements. The National Republican Senatorial Committee issued only a terse statement of congratulations to O'Donnell.

The reaction laid bare the frustration the Republican establishment feels about the perceived lack of pragmatism and political calculation in the tea party movement's approach.

As if to prove the point, tea party favorite Sen. Jim DeMint (R-S.C.) said Wednesday: "I don't want the majority back if we don't believe anything."

The primaries did not prove that Americans had embraced the movement's political philosophy. Its clearest successes typically came in smaller states, where a band of highly energized activists and a relatively modest investment in television advertising were able to make a big impact.

Running in the general election could moderate positions advanced by tea party-backed candidates. Paul in Kentucky and Angle in Nevada made notable shifts in rhetoric after winning nomination. Angle stopped describing her support for "phasing out" Social Security. Paul has downplayed talk of his libertarian background.

"If you're trying to rebuild a majority coalition, even with the tea party and Republicans, you don't get there," said Republican strategist David Winston. "You need independents."

O'Donnell, a onetime abstinence advocate with no experience in office, is widely expected to have trouble wooing Delaware's moderate and independent voters. And the win for the tea party movement was described by some as a win for Democrats — mostly by gleeful Democrats themselves.

No sooner did O'Donnell declare victory Tuesday than Democratic Party allies began running video of her, as a 1990s Christian activist, appearing on MTV opposing masturbation.

However, it's not clear that is the message moderate voters are taking away from the primary battles.

Polls have found that a significant number of people hold a negative view of the tea party. But those numbers shrink in surveys of those most likely to vote. In a CBS poll released Wednesday, nearly half of registered voters polled said they did not know enough about the movement to have an opinion.

That may be one reason that tea party candidates are holding their own. In Kentucky, Paul has maintained a lead over Democrat Jack Conway, despite controversy over Paul's civil rights views. Paul had said the government shouldn't force businesses to follow civil rights laws, but later declared his support for the 1964 Civil Rights Act. In Nevada, a swing state with a large number of independents, perennial activist Angle is running neck-and-neck with Senate Majority Leader Harry Reid.

The Republican leadership's job now is to find a message that unites both wings of the party, Winston said.